1.5.1: Preparation N.5

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(1) Determine which of the following fractions are equivalent to $\dfrac{3}{4}$. Select all that apply.

(i) $\dfrac{15}{20}$

(ii) $\dfrac{6}{9}$

(iii) $\dfrac{24}{32}$

(iv) $\dfrac{75}{100}$

(v) $\dfrac{9}{16}$

(2) Mary is preparing for a party. She wants to create a snack mix that consists of 4 parts of M&M’s to 7 parts of peanuts. List three possible combinations that would be an acceptable mixture of M&M’s and peanuts.

(3) Solve the following equations for n:

(a) $\dfrac{80}{125} = \dfrac{n}{250}$

(b) $\dfrac{31.5}{n} = \dfrac{3.5}{540}$

(4) In May of 2023, the exchange rate was reported to be 1 U.S. Dollar ($) = 0.93 Euros (€). How many Euros are equivalent to $450? The Euro is divided into 100 cents. Round to the nearest cent.

(5) The population density of Martin County, Minnesota is reported to be 28 people/mi2. The county has a total area of 712 square miles. How many people would you expect to be living in this county?

One usually needs to take special care when comparing dollar amounts over time, as the following scenarios illustrate.

Scenario I

According to the U.S. Bureau of Labor Statistics (BLS), the average cost of white bread in the United States in 1980 was $.50 per pound while in 2022 it was $1.99 per pound.

(6) Does the rise in the cost of bread from 1980 to 2022 mean that bread is no longer affordable? Explain.

Scenario II

When Carlotta was a college student, she decided that after paying tuition and living expenses she could usually afford to go out to dinner and a movie once every other week. Now that she has graduated, she feels that she can afford dinner and a movie at least once a week.

(7) Does this mean that the cost of dinner and a movie has decreased over time? Explain.

(8) An online article²⁰, posted in 2020 looked at the prices of twenty-four popular video game consoles. It shows both the original price of the console, as well as the price adjusted for inflation in 2020.

Use data below for consoles released since 2000 to answer the following questions.

Console	Year	Original Price	2020 Price
PlayStation 2	2000	$299	$446.64
GameCube	2001	$199	$291.57
Xbox	2001	$299	$438.08
Xbox 360	2005	$299	$393.30
Wii	2006	$249	$321.19
PlayStation 3	2006	$499	$643.67
Wii U	2012	$299	$337.57
PlayStation 4	2013	$399	$444.96
Xbox One	2013	$499	$556.48
PlayStation 4 Pro	2016	$399	$429.69
Nintendo Switch	2017	$299	$318.77
Xbox One X	2017	$499	$525.80
Nintendo Switch Lite	2019	$199	$201.45
Xbox Series S/X	2020	$299	$299
PlayStation 5 Digital/Disc	2020	$399	$399

(a) Identify the two cheapest consoles by original price.

(b) Identify the three most expensive consoles by original price.

(d) Identify the two most expensive consoles by adjusted price.

In the next collaboration, we will be comparing the U.S. national debt at different periods in time. The first step is to make sure that all the dollar amounts are expressed in comparable terms. The following table gives estimates of the U.S. national debt at various times in history.

Year	U.S. National Debt
1860	$64.8 million
1945	$259 billion
1980	$930 billion
1995	$4.974 trillion
2010	$14.025 trillion
2021	$28.429 trillion

(9) In order to better compare these quantities, convert all dollar amounts to billions of dollars.

Year	U.S. National Debt
1860
1945
1980
1995
2010
2021

(10) Based on this information, does it appear that the U.S. national debt continues to grow year after year? Write one reason why a person might say that the debt is not really growing during this period?

(11) In the next collaboration, we will be using the Consumer Price Index (CPI). Use the Investopedia site to learn about the CPI: https://www.investopedia.com/terms/c/consumerpriceindex.asp

How would you define what the CPI is?

After Preparation N.5 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration N.5, you should understand the concepts and demonstrate the skills listed below:

Skill or Concept: I can …	Rating from 1 to 5
convert between millions, billions, and trillions.
solve a proportion.
express one number as a percent of another.
Identify equivalent fractions.

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²⁰ https://www.ign.com/articles/comparing-the-price-of-every-game-console-with-inflation

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